Superconductors for

Application in Detector Magnets

Herman ten Kate

1. Critical parameters

2. Practical superconductors

3. Temperature margin

4. Stability criteria

5. Application in Magnets

Superconducting Magnets - why so relevant ?

No power consumption, except for refrigeration

lower power bills

Ampere turns are cheap, so do not need iron,

except for shielding

higher magnetic field

higher energy density or less volume

reduced capital cost

High current density

compact windings

high gradients, high forces

higher particle/beam density

But

Superconductors suffer losses when the magnetic

field changes

rise in temperature, there is not much margin

increase in refrigeration load

Superconductivity = zero DC resistance = no Ohmic loss

1. The critical surface of Niobium Titanium

Niobium titanium, NbTi, is the standard

work horse for superconducting

magnets.

It is a ductile alloy.

The critical surface is the boundary

between superconductivity and

normal resistivity in 3 dimensional

space.

Material is Superconducting below the

surface, and has resistance

everywhere above it.

An upper critical field Bc2 and critical

temperature Tc are characteristic of

the alloy composition.

Critical current density Jc(B,T) depends

on processing.

Cu

rren

t d

ensi

ty (

kA

.mm

-2)

Jc

Tc

Bc2

Filamentary composite wires

For reasons explained later,

superconducting materials are always

used in combination with a good

normal conductor such as copper.

To ensure intimate mixing between the

two, the superconductor is made in

the form of fine filaments embedded in

a matrix of copper.

Typical dimensions are:

• wire diameter = 0.3 - 1.3 mm

• filament diameter = 5 – 50 mm.

For electromagnetic reasons, the

composite wires are twisted so that

the filaments look like a rope.

Cross sections of superconducting wires

40 wires in a cable, surrounded by pure aluminium

Critical temperature and critical magnetic field

sno

c GGB

m2

2

kB is Boltzmann's constant

D(0) is the energy gap (binding

energy of Cooper pairs) of at T= 0.

)0(25.3 DcB Tk

Critical Field Bc:

Type I superconductors show the

Meissner effect. Field is expelled when

sample becomes superconducting.

It costs energy to keep the field out. Critical

field happens when the condensation

energy of the superconducting state is just

equal to the energy penalty of keeping the

field out.

Critical Temperature Tc

where G is the Gibbs Free Energy of

the normal/superconducting state. BCS

theory says 2))0((2/1)0()0( D Fsn NGG

where NF is the density of states at the

Fermi surface of metal in normal state -

calculate it from: 223/2 BF kN

where is Sommerfeld coefficient

of electronic specific heat

3TATC

Critical temperature and critical magnetic field

Combining the previous equations:

ccc TxTB2

1

42

12

1

0 1065.72

5.3

2

3)0(

m

Thermodynamic critical field Bc

so like the critical temperature, Bc

is defined by the chemistry

typically for NbTi ~ 103 J m-3 K-1

so if T= 10 K Bc = 0.24T

Thus: Type I superconductors are

useless for magnets!

Note: Meissner effect is not total, the magnetic field actually penetrates a small

distance l the London penetration depth.

Another characteristic distance is the coherence length z ; the minimum distance

over which the electronic state can change from superconducting to normal.

Critical properties of type II superconductors

Theory of Ginsburg, Landau, Abrikosov & Gorkov

GLAG

defines the ratio k l / x

If k > 1/2 the magnetic field can penetrate in

the form of discrete fluxoids - Type II

a single fluxoid encloses flux

where h = Planck's constant,

e = electronic charge

Weberse

ho

151022

upper

critical field ccBB k22 in the ‘dirty limit' nk

2

1

6104.2

where n is the normal state resistivity ! best superconductors are best resistors !

thus the upper critical field: cnc TB

3

2 101.3

for NbTi: ~ 900 J m -3 K-2 n ~ 65 x10 -8 W m Tc = 9. K hence Bc2 = 18.5 T

h / 2e

I

Critical current density

Flux lines consist of resistive cores with

super-currents circulating round them.

spacing between the flux lines

TatnmB

d o 5223

2 21

a uniform distribution of flux lines gives no net

current, so Jc= 0,

but a gradient produces a net current density

co JJxB m

• gradients must be produced by

inhomogeneities in the material, like

dislocations or precipitates

• process is known as flux pinning

• flux pinning is an irreversible lossy process

precipitates of a Ti in NbTi

Flux lines lattice at 5 T on the same

scale.

Critical properties summary

• Critical temperature: choose the right

material to have a large energy gap or

'depairing energy‘.

• Critical magnetic field: choose a Type

II superconductor with a high critical

temperature and a high normal state

resistivity.

• Critical current density: mess up the

microstructure by cold working and

precipitation heat treatments, the way

in which we have any control.

Similar effects in high

temperature

superconducting materials:

flux line lattice in BSCCO.

MgB2

Upper critical magnetic field of metallic superconductors

Of all metallic

superconductors,

only NbTi is ductile.

Others are brittle inter-

metallic compounds.

Of all superconductors,

only a few are successful !

Meaning: you can make a

wires for acceptable cost.

Critical temperature [K]

Engineering current density

wirescerconeng Jareacellunit

currentJ ll sup

In designing a magnet, what

really matters is the overall

engineering current density Jeng

where λ = area ratio of matrix to superconductor

typically:

for NbTi λ = 1.5 to 3.0 λsc = 0.4 to 0.25

for Nb3Sn λ ~ 3.0 λsc ~ 0.25

for B2212 λ = 3.0 to 4.0 λsc = 0.25 to 0.2

λwire takes account of space occupied by insulation,

cooling channels, mechanical reinforcement etc

and is typically 0.7 to 0.8

)ll

1

1scfill factor in the wire:

NbTi

Cu

insulation

So typically Jeng is only 15% to 30% of Jsupercon

Screening currents and the critical state model

Usual model is a superconducting slab in a

changing magnetic field By

• assume it is infinitely long in the z and y

directions - simplifies to a 1d-problem

• dB/dt induces an electric field E which

causes screening currents to flow at critical

current density Jc

Critical state model or Bean model:

• in a 1d infinite slab geometry, Maxwell's

equation says

B

J

J

x

When a superconductor is subjected

to a changing magnetic field,

screening currents are induced.

Screening currents are in addition to

the transport current, which comes

from the power supply.

They are like eddy currents but, there

is no resistance, they don't decay.

cozoy

JJx

Bmm

A uniform Jc means a constant field

gradient inside the superconductor.

Everywhere in the superconductor the

current density is either Jc or zero.

The flux penetration process

B

field increasing from zero field decreasing through zero

plot field profile across the slab

fully penetrated

• Superconducting magnets do not use power (dc), but need to be cooled.

• They produce high magnetic fields - but in changing fields they suffer ac loss.

• Two types of superconductor

- type I: not suitable for high field

- type II: good for high field - but must work hard to get current density.

• All magnets use type II, usually NbTi (even 50 years after its discovery).

• Performance of superconductors is described by the critical surface in the B T J

space

- properties in B and T space are reversible, determined by the chemistry,

- properties in J space are irreversible and lossy, determined by flux pinning

inhomogeneities.

• Engineering current density is what counts for magnet performance.

• A changing magnet field induces persistent currents in superconductors.

• Persistent currents can be described by the Critical State model,

- they are a major cause of ac loss.

Conclusion for basic properties

2.1 Practical Conductors, NbTi

Very well developed

~1 € / kA m

Cubic alloy, isotropic

Tc : 11 K

Bc2 : 13 T

History of superconductors inventions

Manufacturing NbTi wires

• Vacuum melting of NbTi billets

• Hot extrusion of the copper

NbTi composite

• Sequence of cold drawing and

intermediate heat treatments

to precipitate α-Ti phases as

flux pinning centres

• For very fine filaments, must

avoid the formation of brittle

CuTi intermetallic compounds

during heat treatment

- usually done by enclosing

the NbTi in a thin Nb shell

• Twisting to avoid coupling

2.2 Nb3Sn wires, 3 routes to make it

Bronze Route, Bruker EAS

Internal Tin, Oxford OST

NbSn2 Powder in Tube, Bruker EAS

All Nb3Sn by thermal diffusion of Sn to Nb after coil winding.

~ 1000 A/mm2 (bronze)

~ 3000 A/mm2 (IT/PIT)

at 12T and 4.2 K

Well developed,

still improving

~ 5-25 €/kA m

Tc : 18 K

Bc2 : 30 T

Cubic

inter-metallic, isotropic

Generation II: Coated YBCO conductor

Y-Ba-Cu-O (Y-123)

Tc ~ 92 K, basis for new generation

technology(IBAD, RABiTS or ISD)

available already in up to 1 km length.

Generation I: Bi-Sr-Ca-Cu-O

B2223: Tc ~108 K, tape, no wire! R&D

support halted except in Japan.

B2212: Tc ~ 92 K and

can be made as wire !

Modest investments

to further develop,

mainly by Oxford-OST.

2.3 BSCCO and YBCO

Orthorhombic oxide; strongly anisotropic

~ 100-300 €/kA m !

0

10

20

30

40

0 30 60 90 120 Temperature (K)

Fie

ld (

T)

Helium

Nb-Ti

Nb3Sn

MgB2 film

MgB2 bulk

Hydrogen

Neon Nitrogen

BSCCO

YBCO

Cooling liquids

B versus T of superconductors, unique Y123 domain

Irreversibility line!

YBCO is the dream conductor for 5-20 T magnets operating at 50-60 K !

Superconductors for magnets

Y123 in a magnet,

not in // field !

B2211 may do better than Y123 when anisotropy is considered

MgB2 not for high

field magnets but

niche market 1-5T,

4-20K

Nb3Sn

for any magnets

of 9-20T

B2212 or Y123

for DC magnets of 17-40T

provided cost comes down drastically

NbTi

for high field up to 9 T

and 4 K and 11T,1.8 K

Minimum

practical current

density

3. Critical temperature, field dependency

Superconducting Phase (Jc vs. B and T).

So far constant temperature has been assumed

i.e. no heat release in Critical State Model.

For maintaining the superconducting state,

the conductor must operate below the critical

surface determined by critical current, magnetic

field and temperature.

For NbTi the critical area is bounded by:

Tc= 9.2 K; Bc2(0) = 14.5 T

Bc2(T) = Bc2(0) [1 - (T/9.2)1.7] Bc2(4.2K) = 10.7 T

Tc(B) = Tc(0) (1- (B/14.5))0.59 Tc(5T) = 7.16 K

Similar relations are found for Nb3Sn and BSCCO 2212 and 2223.

20

1510

15

10

20

510

3

5

104

105

106

107

temperature(K)

current density(A/cm )

2

Nb Sn3

Nb-Ti

magnetic field(T)

critical J-H-Tsurface

Temperature margin

When a transport current flows, the onset of resistance is

is further reduced from Tc to Tcs, the current sharing temperature

Tcs(B,I) = Tb + (Tc(B) – Tb) (1 - I/Ic) Tcs(5 T,Ic/2 A) = 5.7 K only!

– So we lost a lot of margin from 9.2 K 7.2 K 5.7 K versus 4.4 K.

– At 4.4 K, at 50% Ic and 5 T there is only 1.2 K margin !

– At 75% of Ic we get 0.7 K, so we never can operate very near to Ic !

– Following DT = Q / c(T)

release of energy (heat) from various sources will cause a temperature

rise and thus the superconducting state is very seriously in danger.

– The heat that can be absorbed without reaching Tcs is the enthalpy

difference DH = c(T) dT between Tcs and To .

Effects of disturbances, sources of heat

We can distinguish various sources of heat

Heat pulses, transients

• Flux jumps

• Cracking of resin

• Wire motion; load in µJ/mm3

Continuous heating

• Flux flow

• Losses in pulsed magnets and at fast ramp down

• AC losses at 50Hz, energy applications, due to alternating

current and fields

• Current sharing due to bad sections in the conductor

• Joints between superconductors, usually < n W, no problem

• Synchrotron radiation in accelerators

• Neutron radiation in tokamaks.

Release of heat and extremely low heat capacity

Why is release of heat so critical at 4 K ?

– Heat capacity is strongly T-dependent and

extremely low below 10 K for all materials

– Copper-NbTi composite:

Cp(T)= ((6.8/+43.8)T3+(97.4+69.8 B)T)

mJ/mm3K, which is at 5 T and 40% NbTi in

Cu matrix:

– 2.5 mJ/mm3K at 4.2 K and

– 0.5 mJ/mm3K at 1.9 K !

– 2.5 mJ/mm corresponds to a movement in

a 1 mm wire at 5 T and 500 A of 1 mm only!

Heat release of mJ/mm3 has to be avoided, otherwise magnet will quench

– avoid friction and slip-stick by introducing low friction sliding (kapton films wrapped around wires and cables)

– avoid any displacement, vacuum impregnation of coils

– avoid resin cracks, avoid local stress concentrations at bonded surfaces

Minimum Propagation Zone

Examples of MPZ in a various wires

– In a bare NbTi wire or filament:

take 5 T; 3000 A/mm2; = 6x10-7 Wm; l= 0.1 W/mK; Tc= 7 K

and we find 0.3 mm only

in a 0.3 mm wire this requires about 1nJ to reach Tc !

– NbTi with CuNi matrix would give 3 mm and 0.1 mJ !

– Such wire is extremely sensitive to any heat pulse

Remedy: reduce by using copper matrix (3x10-10 Wm, factor 2000 !)

and increase l by using copper (> 200 W/mK, factor 2000 again !)

Thus we see how wonderful copper is, without copper no sc magnets !

factor 2000 improvement, from mm to few mm and mJ range

for a typical LHC cable we get about 15 mm

and in the ATLAS conductor (600 mm2 pure Al

and 20 kA) we get about 500 mm !

Achieve stable performance: Adiabatic Filament Stability

Field penetration in filaments

– Field penetrates according the Critical State Model

– In the filament magnetic energy is stored

– When disturbed, the heat must be taken up by the

enthalpy of the filament

– A disturbance DT1 will cause a –DJc, so flux

motion, leading to E, this leading to heat and so

again a DT2

– When DT2 > DT1, the process will accelerate and

the flux profile collapses

– Based on simple slab model, the adiabatic stability

criterion is found:

dfil . Jc < (3 c (Tc-To) / mo)1/2

Thus we see a maximum in the filament thickness for

a given current density, to guarantee stability. -r 0 +r

Bext T2 > T1

Adiabatic Filament Stability

Example for NbTi

– Specific heat c = 5600 J/m3; Tc(5T) = 7.2 K, To= 4.2 K

and Jc = 3000 A/mm2, we find ~70 μm.

– Filament diameter must be adapted to the Jc(B).

– Must be much smaller than 70 mm below 5T

(AC applications, transformers).

Consequences:

– Split the NbTi section required for the Ic into many small filaments.

– We see a fundamental requirement for small filaments besides cooling

and application related arguments like reduction of magnetization loss.

– Disadvantages: filaments are now coupled by transverse fields, extra

AC coupling loss requires filament twisting, cost.

Adiabatic Wire Self field Stability

Filaments coupled by self field

– Adiabatic filament stability requires fine filaments in a matrix

These can be de-coupled for transverse fields by twisting

– But are still fully coupled by the self-field

– Again following the CSM, we see the field

penetration profile disturbed by a DT

– Field profile has to change, penetrates deeper,

causing heat dissipation taken up

by the enthalpy up to a certain limit

– Assuming =sc/total ratio and current density J

– We find for the adiabatic self-field criterion:

D.J < (4c (Tc-To)/mo)1/2 f (I/Ic)

where f (I/Ic) = 1/(-0.5 ln(I) – 3/8 + i2/6 - i4/8)

Thus we see a maximum wire diameter for a given Jc and I/Ic

Bsf(I)

Jc

Br(I)

T2 > T1

Self-field Stability: cable examples

ITER cable for central solenoid

– 65 kA at 13.5 T, ~1152 Nb3Sn wires parallel

in a twisted multi-stage cable.

– Cable layout with 5 stages: 1x3x4x4x4x6.

– Wire 0.81 mm, filaments 4 μm.

– the strands take all positions in the cable to

guarantee equal inductance and current

sharing.

LHC type Nb3Sn Rutherford cable

– 33 stands single stage twisted.

– 13 kA at 11 T.

ATLAS cable

– Al stabilized 40 strands Rutherford cable.

– 65 kA at 5 T.

~1152 wires ITER Nb3Sn cable

33 wires LHC-type Nb3Sn cable

40 strands ATLAS BT cable

Conclusion

Due to the very low heat capacity of materials at low temperature heat

production of mJ/mm3 (kJ/m3) will cause quenches in wires and magnets

Premature quenching, training or even worse, permanent degradation are

the dominant factors determining the success of a magnet application

A mature coil design verified with model magnets regarding wire

displacements in combination with impregnation and low friction

techniques is crucial

Various stability criteria were developed and have to be respected

The criteria largely define the shape and internal layout of wires (many thin

filaments in Cu) and cables (many parallel wires, fully transposed) and

the way cooling is applied (edge, bath or internal forced flow cooling)

The next issue is when despite all this a quench occurs, how the magnet can

be switched of safely and resume operation

Why magnets require High Current and Cables

Magnetic field and stored energy

B N.I E B2.Volume

Inductance L N2

Need safe survival from a quench

Energy dump within short time

before conductor burns out

--->Thus low N, high current I

Also Isafe J.E/Vd , kV-range for Vd , with usual current densities this leads to 10-100 kA

Given strand currents of typically 100 to 500A, we need for large scale magnets multi strand cables of 20-1000 strands,

No escape!

43

Scaling: Isafe J x B2 x Volume

44

50m3 LHC dipole 12 kA @ 8.3 T

25 m3 ATLAS solenoid 8 kA @ 2T, 40 MJ

400 m3 HEF detector magnet 20 kA @ 4 T, 2.6 GJ

1000 m3 ITER magnets 40-70 kA @ 10-13T , 50 GJ

0.0001 m3 HF insert model ~ 200 A

2 m3 MRI magnet 200-800 A @ 1-3 T, ~10 MJ

High current conductors are requested

One cannot build large scale magnets from single

NbTi-Nb3Sn-B2212-Y123 wires or tapes

We need superconductors that can be cabled and survive a quench!

45

no

yes

200 A HTS tape

65000 A@5T Al-NbTi/Cu

ATLAS Barrel Toroid @ CERN

Application 1 : Lab magnets and NMR

46

900 MHz

Market of laboratory magnets in many variants up to 20 T at 1.9 K

NMR spectroscopy magnets up to

~ 22 T, 950 MHz

Pushing up to 30 T using HTS

New high field magnets as user facilities

Beyond 20 T systems become too expensive for single labs and we move to user facilities

A new and unique fully superconducting 32 T magnet user facility, YBCO insert pancake coils

A nested HTS coil in an existing twin outsert of NbTi/Nb3Sn

172 A, 619 H, 9 MJ

Under Construction at the NHMFL, test in 2013

When successful, a real breakthrough

47 Courtesy of NHMFL-Tallahassee

Application 2 : Magnetic Resonance Imaging

Medical NMR, MRI for diagnostics ~ 40000 units installed

It works well due to High Quality NbTi and Persistent Mode

Today standard are 1.5 T but mostly 3 T, actively shielded

- Functional MRI for brain research and treatment

- Real time MRI, filming

- Interventional MRI, surgery

Quest for higher resolutions, higher magnetic field, 7 and 9 T

Philips Siemens

48

High-field MRI beyond 3T, 2 examples

9.4 T MRI magnet

90 cm bore and 54 tons

for brain research in combination with PET scanner, to study degeneration processes like Alzheimer and Parkinson decease

11.75 T MRI magnet

at the limit of NbTi at 1.8 K

90 cm bore,

1.48 kA, 338 MJ

5.2 x 5 foot print, 132 tons

Study of central nervous systems “from mice to humans”

Stretching MRI to the limits….

49

Julich Research Center 2009

Neurospin Project at CEA-Saclay

3 : Proton Therapy

Clinic at PSI

Example PSI Switzerland, Comet synchrotron 250 MeV

Medical accelerators providing a p beam for tumor treatment

- 28 p-therapy centers in the world - 8 operational/planned in Europe

2 Options:

- Large scale facility (like Comet) - Single compact station (future)

Quest for high-field compact and cost efficient integrated units

Needs some time but could become the 2nd large scale medical magnet application of superconductivity

Still River

50

4 : Large Hadron Collider

ATLAS

ALICE LHCb

51

14 TeV pp collider, a complex with more than 9000 superconducting magnets by far the largest superconducting system in operation

CMS

The Large Hadron Collider could not be realized without exclusive use of superconductivity and high quality magnets

No Higgs without Superconductivity………

Superconductivity and HE Physics

1232 dipoles magnets for bending

ATLAS and CMS detector magnets

386 quadrupole magnets for focusing

Nb/Cu cavities for

acceleration

~6000 correction magnets

Insertion and Final Focusing magnets

52

53

LHC type I cables NbTi/Cu 28 strands 15.1 mm wide Ic (1.9K, 9T) ~ 20 kA filament size ~ 5 μm

LHC : 7000 km of 12 kA NbTi/Cu cable

54

5 : HEF Detector magnets, ATLAS

A Barrel Toroid, two End Cap Toroids and a Central Solenoid

provide 2 T for the inner detector ~1 T for the muon detectors in blue

20 m diam. x 25 m length

1000 m3 with field

170 t, 90 km superconductor

700 t cold mass

1320 t magnets

20.4 kA at 4.1 T

1.5 GJ stored energy

4.7 K conduction cooled

10 yrs of construction 97-07 The largest trio of toroids ever built

ATLAS in Amsterdam

55

108 Electronic channels

~7000 t Weight

22 m Diameter

44 m Length

56

The First and The Largest

1st Pb wire coil 1912

The First (1912) and The Largest (2007) 0.05 m and 25 m

6 : Base load e-power with fusion

Advantages Large scale and limitless fuel Available all over the world No greenhouse gases and safe No long-lived radioactive waste

Since 1979, worldwide 7 sc tokamaks (213 in total), 3-8 T on plasma

Recent superconducting machines: KSTAR-Korea, EAST-China, SST1-India

2 under construction: JT60SA and ITER

and 1 Wendelstein type W7X

57

ITER magnet system

58

Major plasma radius 6.2 m 840 m3 plasma and 15 mA current Fusion power: 500 MW

First results medio 2025

ITER: NbTi and Nb3Sn, no options DEMO design start soon, still NbTi & Nb3Sn

May be Bi-2212 or YBCO in production plants when multi-kA cables become available and cost has come down drastically........

7 : Motors and Generators with HTS windings

59

36.5 MW ship motor

Conventional 280 t Superconducting 75 t

Example AMSC-USA

SC generators for wind turbines

60

Direct drives saves weight and volume ~½

Makes towers less heavy, cheaper

8 MW unit under development (AMSC)

Interest from European companies growing

8 : Fault Current Limiter using Bi-2212 bulk

Resistive type

Switching bulk

Bi-2212 bifilar coils to

resistive state

61

10MVA

9 : SC Cable 6 km Amsterdam cable under study

62

Challenge in length never done before

Requires adapted cooling system and perfect vacuum system

Would be nice to see this happening, a real breakthrough

10 : Superconducting JR-MAGLEV in Japan

JR-Maglev since 1969 pushed forward, records at 580 km/h, nominal 500 km/h

Summer 2011 : Now first passengers track will be built, very important!

From Tokyo via Nagoya (in 2027) to Osaka (in 2045) in 1h (now 2h25)

63

Market of Superconductors

~ 5 B€/yr business, growing

today dominated by MRI and Research Magnets, including NMR and accelerator magnets, >90 %

and workhorse superconductors NbTi and Nb3Sn >90 % 64

From materials to magnets

How to make performing multi-kA conductors that guarantee the magnet not to quench or degrade ?

---> We need to understand and control the entire chain

An under developed area of research, but essential to avoid surprises and degraded magnet performance

Striking examples exist of missing understanding putting large projects at risk

65

Sn Nb

20 µm

Filament Lattice

50 nm

Wire

1 mm 35 meter

Magnet

50 mm

Cable

Conclusion

Kamerlingh-Onnes’ invention has given us unique new facilities

in Science : High Field labs, NMR, High Energy Physics, Fusion

in Medicine : MRI imaging and medical accelerators

in Transport : Maglev

and more…

Superconductors are very successfully applied where no alternatives are present (magnets >2 T and in a large volume >1 L)

After 25 years of development, High Temperature Superconductors are also available in km lengths, still a long way to go, to make them cheaper, but their properties are shiny and irresistible.....

A very exciting world of science and technology………..

66